Abstract This thesis aims to evaluate networking aspects of autonomous packets access systems when dynamically and adaptively performing resource and network management. In this context, Quality of Service (QoS)-aware solutions for resource sharing and control (e.g., channel access, load control, interference management and routing techniques among others) in large-scale wireless networks are envisaged. We propose and investigate distributed coordination mechanisms for controlling the co-channel interference generated in multi-tier coexistence scenarios consisting of macrocells underlaid with short-range small cells. The rationale behind employing such mechanism is to opportunistically reuse resources without compromising ongoing transmissions on the overlaid macrocells, while still guaranteeing QoS in both tiers. To mitigate the resulting co-channel interference, the underlaid tiers of small cells use distributed mechanism that relies on minimal signaling exchange, e.g., the Time Division Duplexing (TDD)-underlay approach which is based on regular busy tones. Herein, stochastic geometry is used to model network deployments, while higherorder statistics through the cumulants concept is utilized to characterize the probability distribution of the aggregate interference at the tagged receiver. To conduct our studies, we consider a shadowed fading channel model incorporating log-normal shadowing and Nakagami-m fading. In addition, various network algorithms, such as power control and frequency (re)allocation, are included in the analytical framework. To evaluate the performance of the proposed solutions, we also derive closed-form expressions for the outage probability and average spectral efficiency with respect to the receiver of interest under various channel conditions and network configurations. Results show that the analytical framework matches well with numerical results obtained from Monte Carlo simulations, and that the coordination mechanisms substantially improve the performance of overlaid macrocell networks, while also benefiting small cells. In contrast to the uncoordinated Frequency Division Duplexing mode, the coordinated TDD-underlay solution shows a reduction in the outage probability, while the average spectral efficiency increases at high loads. Although more elaborated interference control techniques such as, downlink bitmap and distributed antennas systems become needed, when the density of uncoordinated small cells in the underlaid tier gets high. / Tiivistelmä Tämä väitöskirja pyrkii arvioimaan autonomisia pakettikytkentäisiä järjestelmiä verkon näkökulmasta, kun resurssien ja verkon hallinta tapahtuu dynaamisesti ja adaptiivisesti. Tässä yhteydessä suunnitellaan QoS-tietoisia ratkaisuja resurssien jakamiseen ja hallintaan (esim. kanavan allokointi, kuorman hallinta, häiriön käsittely ja reititystekniikat) suuren skaalan langattomiin verkkoihin. Ehdotamme ja tutkimme hajautettuja koordinointimekanismeja monikanavien häiriöiden hallintaan monitasoisissa skenaarioissa, jotka koostuvat lyhyen kantaman soluista makrosoluissa. Peruste näille mekanismeille on resurssien opportunistinen uudelleenkäyttö tinkimättä käynnissä olevista lähetyksistä suuremmissa makrosoluissa, samalla kun QoS taataan molemman tason lähetyksissä. Pienentääkseen aiheutuvaa monikanavahäiriöitä, alemman tason pienet solut käyttävät hajautettua mekanismia, kuten esimerkiksi säännöllisiin varattu-ääniin perustuvaa Time Division Duplexing (TDD) - mekanismia, vähällä signaalien vaihdon määrällä. Stokastista geometriaa käytetään mallintamaan verkkoja, kun taas korkeamman tason tilastollista laskentaa kumulanttimenetelmän käsitteen kautta käytetään kuvaamaan kokonaishäiriön todennäköisyysjakaumaa merkityssä vastaanottimessa. Käsittelemme varjostuvaa ja häipyvää kanavamallia sisältäen log-normaalin varjostumisen ja Nakagamim häipymisen. Lisäksi sisällytämme analyyttiseen työhön monenlaisia verkkoalgoritmeja tehohallintaan ja taajuuden (uudelleen)allokointiin. Ehdotettujen ratkaisujen tehokkuuden arvioimiseksi johdamme myös suljetut muodot katkosten todennäköisyyksille ja keskimääräiselle spektrin käytön tehokkuudelle halutun vastaanottimen suhteen monissa kanavatiloissa ja verkon kokoonpanoissa. Tulokset osoittavat, että analyyttisen työn tulokset vastaavat hyvin Monte Carlo - simulaatioilla saatujen numeeristen tulosten kanssa ja että koordinointimekanismit parantavat makrosoluverkkojen tehokkuutta merkittävästi, samalla kun myös pienet solut hyötyvät. Toisin kuin koordinoimaton Frequency Division Duplexing -toimintatila, koordinoitu TDD-toimintatila pienentää katkosten todennäköisyyttä samalla kun keskimääräinen spektrin käytön tehokkuus kasvaa suurella kuormalla. Toisaalta kehittyneemät häiriönhallintatekniikat, kuten alalinkki bittikartta sekä hajautetut antennijärjestelmät, tulevat tarpeelliseksi, kun pienten koordinoimattomattomien solujen tiheys kasvaa alemmalla tasolla.

Abstract This thesis focuses on THz band channel modeling and characterization. This vast frequency band spans from 100 GHz to 10 THz. The approximately 10,000 GHz bandwidth together with advances in THz capable electronics have made this band highly potential for many future applications, e.g., imaging and nanodevice-to-nanodevice communications. The latter is the reference application of this thesis and it focuses on the communication among very small and simple devices. The main focus of the thesis is on the THz channel characterization. Therefore, the channel models presented herein are also suitable for communications at macroscopic scale. The THz band offers opportunities, but has many problems as well. One of these is molecular absorption, which causes frequency selective fading to signals. The fading is caused by the signals’ energy absorption in the resonance frequencies of the molecules in the communication medium. Based on the conservation of energy, the absorption is understood to cause a new type of noise in the THz links: transmission induced noise. This noise component is analyzed from multiple physical viewpoints. The THz signals have short enough wavelengths to theoretically allow scattering on aerosols in the atmosphere. Scattering causes frequency dependent loss of the signals, but also a signal spread in time over multiple scattering events. It is shown here that in some specific atmospheric conditions the scattering causes signal loss and time spread. In addition to the theoretical channel models, measurements on a variety of propagation phenomena are con- ducted and analyzed. These include penetration losses, rough surface reflections and scattering, and diffraction. Through the measurements, it can be shown that the THz band communications is feasible in non-line-of-sight (NLOS) conditions in spite of the above phenomena. In the last part of this thesis, stochastic geometry is applied to the THz band in order to estimate the mean interference power and outage probabilities in dense networks formed from nanodevices. Because of the large losses in the channel, large interference levels require large numbers of devices. Stochastic geometry offers perfect tools to estimate the mean interference, and also in the case of directional antennas, which are most likely implemented in all the THz band devices due to large power losses in the channel. / Tiivistelmä Tämä väitöskirja paneutuu THz-taajuisien kanavien mallintamiseen. Tämä valtavan laaja kaista ulottuu sadasta gigahertsistä aina kymmeneen terahertsiin asti. Noin 10000 GHz:n kaistanleveys, yhdistettynä THz-taajuudet mahdollistavien elektroniikan komponenttien kehitykseen, tekee tästä kaistasta erittäin houkuttelevan vaihtoehdon moniin tulevaisuuden sovelluksiin. Näitä ovat mm. kuvantaminen ja nanolaitteiden välinen tietoliikenne. Viimeisin on tämän väitöskirjan viitekehys ja keskittyy hyvin pienien ja yksinkertaisien laitteiden väliseen viestintään. Työn keskittyy pääosin THz-kanavamallinnukseen, joten esitettyjä tuloksia voidaan hyödyntää myös nanoskaalaa suuremmissa verkoissa. THz-taajuudet avaavat mahdollisuuksia, mutta tuovat myös ongelmia. Yksi näistä on molekulaariabsorptio, joka aiheuttaa taajuusselektiivistä häipymää signaaleihin. Tämä ilmiö johtuu sähkömagneetisen energian absorbotumisesta ilman molekyylien resonanssitaajuuksilla. Sen on myös arveltu johtavan uudenlaisen kohinan syntyyn, lähetysten indusoimaan kohinaan, perustuen energian säilymislakiin. Lähetysten indusoimaa kohinaa tutkitaan tässä työssä erilaisista fysikaalisista näkökulmista. THz-taajuisen säteilyn aallonpituus on riittävän lyhyt mahdollistamaan sironta ilmassa olevista aerosoleista. Sironta aerosoleista johtaa taajusriippuvaan signaalitehon häviöön, mutta myös signaalitehon leviämiseen ajassa monisironnan kautta. Työssä todennetaan, että sopivissa olosuhteissa sironta lisää häviöitä ja viivehajetta kanavassa. Teoreettisten kanavamallien lisäksi analysoidaan mittauksin alemmilta taajuusalueilta tuttuja etenemisilmiöitä, kuten signaalin läpäisyä, heijastuksia ja sirontaa pinnoilta, sekä diffraktioita. Mittausten kautta voidaan näyttää, että THz-taajuinen tiedonsiirtolinkki voidaan luoda myös ilman näköyhteyttä yllä mainittujen ilmiöiden kautta. Työn viimeisessä osassa sovelletaan stokastista geometriaa THz-taajuuksille keskimääräisen häiriötehon ja toimintakyvyttömyystodennäköisyyden selvittämiseksi tiheissä nanolaitteiden muodostamissa verkoissa. Isojen kanavahäviöiden takia suuri häiriötaso vaatii suuren määrän laitteita. Stokastinen geometria antaa täydelliset työkalut häiriötason estimointiin. Tätä voidaan myös hyödyntää suuntaavien antennien tapauksessa, joita tullaan suurella todennäköisyydellä käyttämään kaikissa THz-laitteissa johtuen suurista signaalihäviöistä kanavassa.

Orientador: Paulo Regis Caron Ruffino / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-27T10:29:03Z (GMT). No. of bitstreams: 1 Morgado_LeandroBatista_D.pdf: 1320837 bytes, checksum: db1015f01556b3de2b1f7ca1c6bf33d3 (MD5) Previous issue date: 2015 / Resumo: Este trabalho aborda alguns aspectos da teoria de equações diferenciais estocásticas em relação a semimartingales com saltos, suas aplicações na decomposição de fluxos estocásticos em variedades, bem como algumas implicações de natureza geométrica. Inicialmente, em uma variedade munida de distribuições complementares, discutimos o problema da decomposição de fluxos estocásticos contínuos, isto é, gerados por EDE em relação ao movimento Browniano. Resultados anteriores garantem a existência de uma decomposição em difeomorfismos que preservam as distribuições até um tempo de parada. Usando a assim denominada equação de Marcus, bem como uma técnica que denominamos equação 'stop and go', vamos construir um fluxo estocástico próximo ao original, com a propriedade adicional que o fluxo construído pode ser decomposto além do tempo de parada inicial. Em seguida, trataremos da decomposição de fluxos estocásticos no caso descontínuo, isto é, para processos gerados por uma EDE em relação a um semimartingale com saltos. Após uma discussão sobre a existência da decomposição, obtemos as EDEs para as componentes respectivas, a partir de uma extensão que propomos da fórmula de Itô-Ventzel-Kunita. Finalmente, propomos um modelo de equações diferenciais estocásticas com retardo incluindo saltos. A ideia é modelar certos fenômenos em que a informação pode chegar ao receptor por diferentes canais: de forma contínua, mas com retardo, e em tempos discretos, de forma instantânea. Vamos abordar aspectos geométricos relacionados ao tema: transporte paralelo em curvas diferenciáveis com saltos, bem como possibilidade de levantamento de uma solução do nosso modelo de equação para o fibrado de bases de uma variedade diferenciável / Abstract: The main subject of this thesis is the theory of stochastic differential equations driven by semimartingales with jumps. We consider applications in the decomposition of stochastic flows in differentiable manifolds, and geometrical aspects about these equations. Initially, in a differentiable manifold endowed with a pair of complementary distributions, we discuss the decomposition of continuous stochastic flows, that is, flows generated by SDEs driven by Brownian motion. Previous results guarantee that, under some assumptions, there exists a decomposition in diffeomorphisms that preserves the distributions up to a stopping time. Using the so called Marcus equation, and a technique that we call 'stop and go' equation, we construct a stochastic flow close to the original one, with the property that the constructed flow can be decomposed further on the stopping time. After, we deal with the decomposition of stochastic flows in the discontinuous case, that is, processes generated by SDEs driven by semimartingales with jumps. We discuss the existence of this decomposition, and obtain the SDEs for the respective components, using an extension of the Itô-Ventzel-Kunita formula. Finally, we propose a model of stochastic differential equations including delay and jumps. The idea is to describe some phenomena such that the information comes to the receptor by different channels: continuously, with some delay, and in discrete times, instantaneously. We deal with geometrical aspects related with this subject: parallel transport in càdlàg curves, and lifting of solutions of these equations to the linear frame bundle of a differentiable manifold / Doutorado / Matematica / Doutor em Matemática

Les futures applications sans fil anticipent une explosion de la pléthore de cas d'utilisation et de services, qui ne peut être soutenue par des améliorations incrémentielles des schémas de communication existants. Pour cela, deux axes de recherche sont particulièrement intéressants: la densification du réseau à l'aide de petites cellules et la communication par ondes millimétriques (ondes millimétriques). Dans cette thèse, nous modélisons et évaluons des réseaux cellulaires constitués de petites cellules à ondes millimétriques utilisant la technique d'accès multi-radio (RAT) déployées au-dessus de la macro-architecture existante. Premièrement, nous modélisons mathématiquement un déploiement homogène de petites cellules multi-RAT et caractérisons les performances de l'utilisateur et du réseau en termes de probabilité de couverture signal sur brouillage plus rapport de bruit (SINR), de débit descendant et de probabilité de surcharge de cellule. Ensuite, nous étudions l'association des utilisateurs à différents niveaux et la sélection optimale de différents RAT, de manière à optimiser ces mesures de performance. En règle générale, les modèles de réseau cellulaire qui supposent des déploiements homogènes de petites cellules ne tiennent pas compte des nuances des caractéristiques de blocage urbain. Pour résoudre ce problème, nous modélisons les emplacements de petites cellules le long des routes d'une ville, puis nous prenons en compte les blocages de signaux dus à la construction d'immeubles ou au déplacement de véhicules sur les routes. Sur ce réseau, nous supposons que l’opérateur prend en charge trois types de services v.i.z., les communications ultra-fiables à faible temps de latence (URLLC), les communications massives de type machine (mMTC) et le haut débit mobile amélioré (eMBB) avec des besoins différents. En conséquence, nous étudions la sélection optimale de RAT pour ces services avec divers blocages de véhicules. Enfin, sur la base du modèle de déploiement sur route de petites cellules à ondes millimétriques, nous étudions un réseau conçu pour prendre en charge simultanément des services de positionnement et de données. Nous caractérisons la précision du positionnement en fonction des limites de la localisation, puis étudions des stratégies optimales de partitionnement des ressources et de sélection de la largeur de faisceau afin de répondre à diverses exigences de positionnement et de débit de données. / Future wireless applications anticipate an explosion in the plethora of use-cases and services, which cannot be sustained by incremental improvements on the existing communication schemes. For this, two research directions are particularly attractive: network densification using small cells and millimeter wave (mm-wave) wave communications. In this thesis, we model and evaluate cellular networks consisting of multi-radio access technique (RAT) mm-wave small cells deployed on top of the legacy macro-architecture. First, we mathematically model a homogeneous deployment of multi-RAT small cells and characterize the user and network performance in terms of signal to interference plus noise ratio (SINR) coverage probability, downlink throughput, and the cell overloading probability. Then, we study users association to different tiers and optimal selection of different RATs, so as to optimize these performance metrics. Generally, cellular network models that assume homogeneous deployments of small cells fail to take into account the nuances of urban blockage characteristics. To address this, we model the small cell locations along the roads of a city, and subsequently, we take into consideration the signal blockages due to buildings or moving vehicles on the roads. In this network, we assume that the operator supports three types of services v.i.z., ultra-reliable low-latency communications (URLLC), massive machine-type communications (mMTC), and enhanced mobile broadband (eMBB) with different requirements. Consequently, we study the optimal RAT selection for these services with varying vehicular blockages. Finally, based on the on-road deployment model of mm-wave small cells, we study a network designed to support positioning and data services simultaneously. We characterize the positioning accuracy based on the localization bounds and then study optimal resource partitioning and beamwidth selection strategies to address varied positioning and data-rate requirements.

In-band full-duplex (FD) communications have been optimistically promoted to improve the spectrum utilization and efficiency. However, the penetration of FD communications to the cellular networks domain is challenging due to the imposed uplink/downlink interference. This thesis presents a tractable framework, based on stochastic geometry, to study FD communications in multi-tier cellular networks. Particularly, we assess the FD communications effect on the network performance and quantify the associated gains. The study proves the vulnerability of the uplink to the downlink interference and shows that the improved FD rate gains harvested in the downlink (up to 97%) comes at the expense of a significant degradation in the uplink rate (up to 94%). Therefore, we propose a novel fine-grained duplexing scheme, denoted as α-duplex scheme, which allows a partial overlap between the uplink and the downlink frequency bands. We derive the required conditions to harvest rate gains from the α-duplex scheme and show its superiority to both the FD and half-duplex (HD) schemes. In particular, we show that the α-duplex scheme provides a simultaneous improvement of 28% for the downlink rate and 56% for the uplink rate. We also show that the amount of the overlap can be optimized based on the network design objective. Moreover, backward compatibility is an essential ingredient for the success of new technologies. In the context of in-band FD communication, FD base stations (BSs) should support HD users' equipment (UEs) without sacrificing the foreseen FD gains. The results show that FD-UEs are not necessarily required to harvest rate gains from FD-BSs. In particular, the results show that adding FD-UEs to FD-BSs offers a maximum of 5% rate gain over FD-BSs and HD-UEs case, which is a marginal gain compared to the burden required to implement FD transceivers at the UEs' side. To this end, we shed light on practical scenarios where HD-UEs operation with FD-BSs outperforms the operation when both the BSs and UEs are FD and we find a closed form expression for the critical value of the self-interference cancellation power required for the FD UEs to outperform HD UEs.

In this thesis, abstract bounds for the normal approximation of Poisson functionals are computed by the Malliavin-Stein method and used to derive central limit theorems for problems from stochastic geometry. As a Poisson functional we denote a random variable depending on a Poisson point process. It is known from stochastic analysis that every square integrable Poisson functional has a representation as a (possibly infinite) sum of multiple Wiener-Ito integrals. This decomposition is called Wiener-Itô chaos expansion, and the integrands are denoted as kernels of the Wiener-Itô chaos expansion. An explicit formula for these kernels is known due to Last and Penrose. Via their Wiener-Itô chaos expansions the so-called Malliavin operators are defined. By combining Malliavin calculus and Stein's method, a well-known technique to derive limit theorems in probability theory, bounds for the normal approximation of Poisson functionals in the Wasserstein distance and vectors of Poisson functionals in a similar distance were obtained by Peccati, Sole, Taqqu, and Utzet and Peccati and Zheng, respectively. An analogous bound for the univariate normal approximation in Kolmogorov distance is derived. In order to evaluate these bounds, one has to compute the expectation of products of multiple Wiener-Itô integrals, which are complicated sums of deterministic integrals. Therefore, the bounds for the normal approximation of Poisson functionals reduce to sums of integrals depending on the kernels of the Wiener-Itô chaos expansion. The strategy to derive central limit theorems for Poisson functionals is to compute the kernels of their Wiener-Itô chaos expansions, to put the kernels in the bounds for the normal approximation, and to show that the bounds vanish asymptotically. By this approach, central limit theorems for some problems from stochastic geometry are derived. Univariate and multivariate central limit theorems for some functionals of the intersection process of Poisson k-flats and the number of vertices and the total edge length of a Gilbert graph are shown. These Poisson functionals are so-called Poisson U-statistics which have an easier structure since their Wiener-Itô chaos expansions are finite, i.e. their Wiener-Itô chaos expansions consist of finitely many multiple Wiener-Itô integrals. As examples for Poisson functionals with infinite Wiener-Itô chaos expansions, central limit theorems for the volume of the Poisson-Voronoi approximation of a convex set and the intrinsic volumes of Boolean models are proven.

Cette thèse explore le caching proactif, l'un des principaux paradigmes des réseaux cellulaires 5G utilisé en particulier le déploiement des réseaux à petites cellules (RPCs). Doté de capacités de prévisions en combinaison avec les récents développements dans le stockage, la sensibilité au contexte et les réseaux sociaux, le caching distribué permet de réduire considérablement les pics de trafic dans la demande des utilisateurs en servant de manière proactive ces derniers en fonction de leurs demandes potentielles, et en stockant les contenus à la fois dans les stations de base et dans les terminaux des utilisateurs. Pour montrer la faisabilité des techniques de caching proactif, nous abordons le problème sous deux angles différents, à savoir théorique et pratique.Dans la première partie de cette thèse, nous utiliserons des outils de géométrie stochastique pour modéliser et analyser les gains théoriques résultant du stockage dans les stations de base. Nous nous focalisons en particulier sur 1-) les réseaux ``niveau-simple" dans lesquels de petites stations de base ayant une capacité de stockage limitée, 2-) Réseaux ``niveau-multiples" avec un backbone à capacité limitée et 3-) Les réseaux ``niveau-multiples groupés" à deux topologies différentes: déploiements en fonction de la couverture et en fonction de la capacité. Nous y caractérisons les gains de stockage en termes de débit moyen fourni et de délai moyen, puis nous montrons différents compromis en fonction du nombre de stations de base, de la taille de stockage, du facteur de popularité des contenus et du débit des contenus ciblés. Dans la seconde partie de la thèse, nous nous focalisons à une approche pratique du caching proactif et nous focalisons sur l'estimation du facteur de popularité des contenus et les aspects algorithmiques. En particulier, 1-) nous établissons dans un premier lieu les gains du caching proactif à la fois au niveau des stations de base qu'au niveau des terminaux utilisateurs, en utilisant des outils récents d'apprentissage automatique exploitant le transfert des communications appareil-à-appareil (AàA); 2-) nous proposons une approche d'apprentissage sur la base de la richesse des informations transmises entre terminaux (que nous désignons par domaine source) dans le but d'avoir une meilleure estimation de la popularité des différents contenus et des contenus à stocker de manière stratégique dans les stations de base (que nous désignons par domaine cible); 3-) Enfin, pour l'estimation de la popularité des contenus en pratique, nous collectons des données de trafic d'usagers mobiles d'un opérateur de télécommunications sur plusieurs de ses stations de base pendant un certain nombre d'observations. Cette grande quantité de données entre dans le cadre du traitement ``Big Data" et nécessite l'utilisation de nouveaux mécanismes d'apprentissage automatique adaptés à ces grandes masses de données. A ce titre, nous proposons une architecture parallélisée dans laquelle l'estimation de la popularité des contenus et celle du stockage stratégique au niveau des stations de base sont faites simultanément. Nos résultats et analyses fournissent des visions clés pour le déploiement du stockage de contenus dans les petites stations de base, l'une des solutions les plus prometteuses des réseaux cellulaires mobiles hétérogènes 5G. / This thesis explores one of the key enablers of 5G wireless networks leveraging small cell network deployments, namely proactive caching. Endowed with predictive capabilities and harnessing recent developments in storage, context-awareness and social networks, peak traffic demands can be substantially reduced by proactively serving predictable user demands, via caching at base stations and users' devices. In order to show the effectiveness of proactive caching techniques, we tackle the problem from two different perspectives, namely theoretical and practical ones.In the first part of this thesis, we use tools from stochastic geometry to model and analyse the theoretical gains of caching at base stations. In particular, we focus on 1) single-tier networks where small base stations with limited storage are deployed, 2) multi-tier networks with limited backhaul, and) multi-tier clustered networks with two different topologies, namely coverage-aided and capacity-aided deployments. Therein, we characterize the gains of caching in terms of average delivery rate and mean delay, and show several trade-offs as a function of the number of base stations, storage size, content popularity behaviour and target content bitrate. In the second part of the thesis, we take a more practical approach of proactive caching and focus on content popularity estimation and algorithmic aspects. In particular: 1) We first investigate the gains of proactive caching both at base stations and user terminals, by exploiting recent tools from machine learning and enabling social-network aware device-to-device (D2D) communications; 2) we propose a transfer learning approach by exploiting the rich contextual information extracted from D2D interactions (referred to as source domain) in order to better estimate the content popularity and cache strategic contents at the base stations (referred to as target domain); 3) finally, to estimate the content popularity in practice, we collect users' real mobile traffic data from a telecom operator from several base stations in hours of time interval. This amount of large data falls into the framework of big data and requires novel machine learning mechanisms to handle. Therein, we propose a parallelized architecture in which content popularity estimation from this data and caching at the base stations are done simultaneously.Our results and analysis provide key insights into the deployment of cache-enabled small base stations, which are seen as a promising solution for 5G heterogeneous cellular networks.

Multi-tier cellular networks have led to a paradigm shift in the deployment of base stations (BSs) where macrocell BSs are overlaid with smaller and lower power BSs such as microcells, picocells, and femtocells. Stochastic geometry has been proven to be an effective tool to capture such heterogeneity and uncertainties in deployment of cellular BSs. In stochastic geometry, random spatial models are used to model multi-tier cellular networks where the locations of BSs is each tier is assumed to be drawn from a point process with the appropriate spatial density. This thesis proposes stochastic geometry-based approaches to analyze, model, and optimize multi-tier cellular networks under several setups and technologies. First, I propose a novel location-aware cross-tier cooperation scheme that aim at improving the performance of users with low signal-to-interference-plus-noise ratio (SINR). Second, I study the performance of cognitive device-to-device (D2D) communication in multi-channel downlink-uplink cellular network with energy harvesting. For the coexistence between cellular and D2D transmissions, I propose a spectrum access policy for cellular BSs to avoid using D2D channels when possible. Third, I investigate the feasibility of energy harvesting from ambient RF interference in multi-tier uplink cellular networks. For this setup, I capture randomness in the network topology and the battery dynamics. Fourth, I extend multi-tier uplink cellular networks to consider the case when users do not necessarily associate with the nearest BS (i.e., flexible cell association). Finally, I compare between different cell association criteria including coupled and decoupled cell association for uplink and downlink transmissions in multi-tier full-duplex cellular networks. For all network setups, I use stochastic geometry to derive simple and closed-form expressions to evaluate the performance in terms of several metrics, e.g., outage probability, mean rate, transmission probability, success probability, and load per BS. I also highlight main tradeoffs in different networks and provide guidelines to optimize different performance metrics by carefully tuning fundamental network design parameters. / February 2017

L'objectif de cette thèse est d'étudier certains aspects des réseaux coopératifs sans fils à l'aide de la géométrie stochastique. Ça permets de considérer la distribution spatiale aléatoire des utilisateurs et les effets adverses de leur interaction, comme l’interférence.Nous étudions la performance, évaluée par la probabilité d'outage, atteignable dans un canal de relai full-duplex quand les nœuds opèrent dans un grand réseau sans fils où les émetteurs interférants sont modelés avec un processus ponctuel de Poisson homogène. Nous trouvons la probabilité d'outage des protocoles décodez-et-renvoyez (decode-and-forward, DF), et comprimez-et-renvoyez (compress-and-forward) et nous faisons une comparaison avec une transmission point à point et un protocole DF half-duplex. Ensuite, nous étudions une situation plus générale dans laquelle les émetteurs qui causent l'interférence peuvent aussi utiliser un relai ou faire des transmissions point à point. Nous étudions la relation entre les avantages de la cooperation et l'interférence qu'elle même génère.Dans la deuxième partie nous étudions la performance des stratégies de partage de vidéos par communications entre dispositifs mobiles (device-to-device, D2D) hors de la bande des communications cellulaires. Nous étudions la fraction des demandes de vidéos qui peuvent être satisfaites par D2D, c’est-à-dire, par le biais des émissions locales, plutôt que par la station de base. Pour étudier ce problème, nous introduisons un modèle de processus ponctuel, qui considère la stratégie de stockage dans les utilisateurs, le problème de comment lier les utilisateurs et les problèmes de la transmission et coordination entre les utilisateurs. / The main goal of this work is to study cooperative aspects of large wireless networks from the perspective of stochastic geometry. This allows the consideration of important effects such as the random spatial distribution of nodes, as well as the effects of interference and interference correlation at receivers, which are not possible when a single link is considered in isolation.First, some aspects of the performance of the relay channel in the context of a large wireless network are considered. Mainly, the performance, in terms of outage probability (OP), of a single full-duplex relay channel utilizing decode-and-forward (DF) or compress-and-forward, when the interference is generated by uniform spatial deployment of nodes, modeled as a Poisson point process. The OP performance of these two protocols is compared with a point-to-point transmission and with a half-duplex DF protocol. Afterwards, the case in which more than one transmitter in the network may use a relay is considered. The effects of cooperation versus interference are studied, when the users use either full-duplex DF, or point-to-point transmissions. In a second phase, this work explores the advantages that could be obtained through out-of-band device-to-device (D2D) video file exchanges in cellular networks. These advantages are measured in terms of the fraction of requests that can be served in a time-block through D2D, thus avoiding a downlink file transfer from the base station. For this, a stochastic geometry framework is introduced, in which the user file-caching policy, user pairing strategy, and link quality and scheduling issues are considered.

Une mosaïque de Poisson-Voronoï est une partition aléatoire de l'espace euclidien en polyèdres, appelés cellules, obtenue à partir d'un ensemble aléatoire discret de points appelés germes. A chaque germe correspond une cellule, qui est l'ensemble des points de l'espace qui sont plus proches de ce germes que des autres germes. Ces modèles sont souvent utilisées dans divers domaines tels que la biologie, les télécommunications, l'astronomie, etc. Les caractéristiques de ces mosaïques et des cellules associées ont été largement étudiées dans l'espace euclidien mais les travaux sur les mosaïques de Voronoï dans un cadre non-euclidien sont rares.Dans cette thèse, on étend la définition de mosaïque de Voronoï à une variétériemannienne de dimension finie et on s'intéresse aux caractéristiques des cellules associées. Plus précisément, on mesure dans un premier temps l'influence que peut avoir la géométrie locale de la variété, c'est-à-dire les courbures sur les caractéristiques moyennes d'une cellule, comme son volume ou son nombre de sommets, en calculant des développements asymptotiques des ces caractéristiques moyennes à grande intensité. Dans un deuxième temps, on s'interroge sur la possibilité de retrouver la géométrie locale de la variété à partir des caractéristiques combinatoires de la mosaïque sur la variété. En particulier, on établit desthéorèmes limites, quand l'intensité du processus des germes tend vers l'infini, pour le nombre de sommets de la mosaïque dans une fenêtre, ce qui permet de construire un estimateur de la courbure et d'en donner quelques propriétés.Les principaux résultats de cette thèse reposent sur la combinaison de méthodesprobabilistes et de techniques issues de la géométrie différentielle. / A Poisson-Voronoi tessellation is a random partition of the Euclidean space intopolytopes, called cells, obtained from a discrete set of points called germs. To each germ corresponds a cell which is the set of the points of the space which are closer to this germ than to the other germs. These models are often used in several domains such as biology, telecommunication, astronomy, etc. The caracteristics of these tessellations and cells have been widely studied in the Euclidean space but only a few works concerns non-Euclidean Voronoi tessellation. In this thesis, we extend the definition of Poisson-Voronoi tessellation to a Riemannian manifold with finite dimension and we study the caracteristics of the associated cells. More precisely, we first measure the influence of the local geometry of the manifold, namely the curvatures, on the caracteristics of the cells, e.g. the mean volume or the mean number of vertices. Second, we aim to recover the local geometry of the manifold from the combinatorial properties of the tessellation on the manifolds. In particular, we establish limit theorems for the number of vertices of the tessellation, when the intensity of the process of the germs tends to infinity. This leads to the construction of an estimator of the curvature of the manifold and makes it possible to derive some properties of it. The main results of this thesis relies on the combination of stochastic methods and techniques from the differential geometry theory.